Well, it is still a matter of taste, but I do not find this necklace so horrible. Of course, I would have prefered a more classical necklace, with dazzling diamonds and gems, but the turquoise/gold mix is a good combination (BTW, turquoise and gold jewels were very frequent in the 19th century, which was the apex of classical jewellery... ), and the overall design looks interesting (I would like to see a larger picture, to observe the details of the design and see if it matches the design of the brooch).
I think it is also a good thing that the Queen receives a necklace to match her turquoise and gold brooch. Indeed, the turquoises of this brooch have a very strong, dark shade, and Queen Margrethe had sometimes worn this brooch along with other turquoise jewels of a paler shade, which did not give a very successful impression. Now, Queen Margrethe has a full set, whose different elements perfectly match with each other.
And of course, knowing that the necklace is a gift from Prince Henrik gives this jewel a more special and sentimental dimension! Prince Henrik may deserve some criticism for his sometimes snob attitudes or his thoughtless comments about his royal/princely status, but he has always been a strong and loyal support to the Queen, and these two are still, after 48 years of marriage, visibly still very much in love. And I find it lovely that Prince Henrik wants to show his love to his 'Daisy' by presenting her new jewels, whose designs is also a discreet reminder of their common cultural references and litterary interests.
By the way, Queen Margrethe also wore in her hair one of the branches of her diamond tiara - as she had already done yesterday at Christiansborg's dinner and in Aarhus last week!